All socialists supported the NHS but not all the supporters of the NHS were socialists. Churchill maintained that he had always been a Tory Democrat i.e. supporting the traditional institutions of England whilst improving the condition of the people in the spirit of One Nation.

The 'accepted parameters of socialism' is problematic. Social reform was advocated across the political spectrum so it would be inaccurate to claim that social reform was an issue outside of mainstream politics and deemed unacceptably 'socialist' or that one side was socialist-minded and the other side was completely anti-socialist. The Conservatives hinted at old age pensions at the 1895 election (though they did not implement them). In 1903 Joe Chamberlain advocated social reform as part of his Tariff Reform project. In 1908 the Liberal Asquith became Prime Minister and introduced a considerable number of social reforms (pensions, insurance, unemployment assistance). During his time as a Liberal government minister in Asquith's government Churchill was a very prominent supporter of social welfare on the German/Bismarckian model ('state socialism').

The First World War and the interwar years saw increasing support for government intervention across the political spectrum and by the eve of the Second World War the Conservatives had drawn up plans that one historian has claimed amounts to half of the social reforms contained in the Beveridge Report of 1942 that laid the foundations for the postwar welfare state.

In short, Churchill's support for the NHS is within the tradition of supporting state welfare whilst retaining a mostly capitalist economy. He was not a socialist in the sense of wanting to transform the British economy into workers control or Soviet Communism but he was in favour of 'state socialism'. But then nearly everyone was by this time.